Question: Reduce to lowest terms: $ \dfrac{7}{6} \div - \dfrac{7}{4} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{7}{4}$ is $- \dfrac{4}{7}$ Therefore: $ \dfrac{7}{6} \div - \dfrac{7}{4} = \dfrac{7}{6} \times - \dfrac{4}{7} $ $ \phantom{ \dfrac{7}{6} \times - \dfrac{4}{7}} = \dfrac{7 \times -4}{6 \times 7} $ $ \phantom{ \dfrac{7}{6} \times - \dfrac{4}{7}} = \dfrac{-28}{42} $ The numerator and denominator have a common divisor of $14$, so we can simplify: $ \dfrac{-28}{42} = \dfrac{-28 \div 14}{42 \div 14} = -\dfrac{2}{3} $